SOLUTION: Simplify (rationalize all denominators) 3/[SQRT(5) - 2] I am pretty sure I need to multiply 3/[SQRT(5) - 2] by SQRT(5)+2 / SQRT (5) +2. Which I think would bring me to an

Algebra ->  Square-cubic-other-roots -> SOLUTION: Simplify (rationalize all denominators) 3/[SQRT(5) - 2] I am pretty sure I need to multiply 3/[SQRT(5) - 2] by SQRT(5)+2 / SQRT (5) +2. Which I think would bring me to an       Log On


   

Question 83552: Simplify (rationalize all denominators)
3/[SQRT(5) - 2]
I am pretty sure I need to multiply 3/[SQRT(5) - 2] by SQRT(5)+2 / SQRT (5) +2.
Which I think would bring me to an answer of 3[SQRT(5)+6. I am not sure if i did everything right and am wonder if I came to the correct answer. Thank you.
Found 2 solutions by fongy, Edwin McCravy:
Answer by fongy(1) About Me  (Show Source):
You can put this solution on YOUR website!
Your answer is incorrect. The correct answer should be 3[sqrt(5)+ 2].
However, your approach is correct. GO through the below solution slowly.
The correct steps in getting the answer are:
Step(1): 3/[sqrt(5)- 2]= 3[sqrt(5)+ 2]/([sqrt(5)- 2]x[sqrt(5)+ 2])
--> this step is to mulitipy numerator and denominator by [sqrt(5)+ 2]
Step (2): = 3[sqrt(5)+ 2]/[(sqrt(5))^2 - (2)^2]
--> The denominator is converted into [(sqrt(5))^2 - (2)^2] according to the identities: ([sqrt(5)- 2]x[sqrt(5)+ 2])= [(sqrt(5))^2 - (2)^2]
Step (3): = 3[sqrt(5)+ 2]/[5 - 4]
= 3[sqrt(5)+ 2]/[1]
= 3[sqrt(5)+ 2]
= answer



Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify (rationalize all denominators)
3/[SQRT(5) - 2]
I am pretty sure I need to multiply 3/[SQRT(5) - 2] by SQRT(5)+2 / SQRT (5) +2.
Which I think would bring me to an answer of 3[SQRT(5)+6. I am not sure if i did everything right and am wonder if I came to the correct answer. Thank you.

 
The other tutor saw your 3[SQRT(5)+6 and thought you meant 3[SQRT(5)+6] which
would have been wrong.  However you meant 3×SQRT(5)+6.  So I think you were
right.  Here, let's go through it and see:

3%2F%28sqrt%285%29-2%29 

Multiply by

+%28sqrt%285%29%2B2%29%2F%28sqrt%285%29%2B2%29

3%2F%28sqrt%285%29-2%29×+%28sqrt%285%29%2B2%29%2F%28sqrt%285%29%2B2%29

%28+3%28sqrt%285%29%2B2%29+%29%2F%28+sqrt%285%29%2B2+%29%28sqrt%285%29-2%29  

Multiply the top out and FOIL out the bottom:

%28+3%2Asqrt%285%29%2B6+%29%2F%285-2%2Asqrt%285%29%2B2%2Asqrt%285%29-4%29 

The middle two terms in the bottom cancel, so we have

%28+3%2Asqrt%285%29%2B6+%29%2F%285-4%29 

%28+3%2Asqrt%285%29%2B6+%29%2F1

+3%2Asqrt%285%29%2B6+

Looks like you're right!

Edwin